The child-theme looks – without any entry – already different from the original Genesis Framework.
I just need a few small changes. Because updates of the framework I would like to do this in an own child-tehme.

What are you using as the base for your child theme? Are you using the 2.0 Sample Child Theme or did you create one on your own? Just to be noted, you shouldn’t modify the Genesis Framework files at all.

No, you don’t modify the Genesis Framework! You should be using the Genesis Sample to build your child theme. Go to your my.studiopress.com account on here. Look in the Downloads for the Sample. Use that and only modify those files and not the framework.